Related papers: Structure-Aware Spectral Sparsification via Unifor…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…
The interconnectedness and interdependence of modern graphs are growing ever more complex, causing enormous resources for processing, storage, communication, and decision-making of these graphs. In this work, we focus on the task graph…
We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature…
Uniform sampling of simple graphs having a given degree sequence is a known problem with exponential complexity in the square of the mean degree. For undirected graphs, randomised approximation algorithms have nonetheless been shown to…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
We provide the first online algorithm for spectral hypergraph sparsification. In the online setting, hyperedges with positive weights are arriving in a stream, and upon the arrival of each hyperedge, we must irrevocably decide whether or…
Spatial transcriptomics clustering is pivotal for identifying cell subpopulations by leveraging spatial location information. While recent graph-based methods modeling cell-cell interactions have improved clustering accuracy, they remain…
Hyperspectral image (HSI) clustering is a challenging task due to the high complexity of HSI data. Subspace clustering has been proven to be powerful for exploiting the intrinsic relationship between data points. Despite the impressive…
In the framework of graph property testing, we study the problem of determining if a graph admits a cluster structure. We say that a graph is $(k, \phi)$-clusterable if it can be partitioned into at most $k$ parts such that each part has…
Graph Neural Network (GNN) achieves great success for node-level and graph-level tasks via encoding meaningful topological structures of networks in various domains, ranging from social to biological networks. However, repeated aggregation…
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…
The formation trajectory planning using complete graphs to model collaborative constraints becomes computationally intractable as the number of drones increases due to the curse of dimensionality. To tackle this issue, this paper presents a…
Spectral Clustering (SC) is one of the most widely used methods for data clustering. It first finds a low-dimensonal embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on…
Spectral clustering is a key research topic in the field of machine learning and data mining. Most of the existing spectral clustering algorithms are built upon Gaussian Laplacian matrices, which are sensitive to parameters. We propose a…
Let a graph be observed through a finite random sampling mechanism. Spectral methods are routinely applied to such graphs, yet their outputs are treated as deterministic objects. This paper develops finite-sample inference for spectral…
This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to…
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $\epsilon$-graphs and $k$-NN graphs can lead to poor performance…
Graph Spectral Sparsification (GSS) identifies an ultra-sparse subgraph, or sparsifier, whose Laplacian matrix closely approximates the spectral properties of the original graph, enabling substantial reductions in computational complexity…
We contribute an approach to the problem of locally computing sparse connected subgraphs of dense graphs. In this setting, given an edge in a connected graph $G = (V, E)$, an algorithm locally decides its membership in a sparse connected…